Once you're in orbit (say around the sun), you have to cancel the orbital velocity to fall into the object you're orbiting around. If you point at the sun and a

Once you're in orbit (say around the sun), you have to cancel the orbital velocity to fall into the object you're orbiting around. If you point at the sun and accelerate 1 km/s directly at it, you're still moving 30 km/s "sideways". All you'd end up doing is making the orbit more elliptical-shaped. At least that's how I see it, but I am far from being an authority on this topic.